Supersymmetry and cotangent bundle over non-compact exceptional Hermitian symmetric space

Abstract

Abstract We construct $$ \mathcal{N}=2 $$ N = 2 supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces $$ \mathrm{\mathcal{M}}={E}_{6\left(-14\right)}/\mathrm{SO}(10)\times \mathrm{U}(1) $$ ℳ = E 6 − 14 / SO 10 × U 1 and E 7(−25) /E 6 × U(1). In order to construct them we use the projective superspace formalism which is an $$ \mathcal{N}=2 $$ N = 2 off-shell superfield formulation in four-dimensional space-time. This formalism allows us to obtain the explicit expression of $$ \mathcal{N}=2 $$ N = 2 supersymmetric nonlinear sigma models on the cotangent bundles over any Hermitian symmetric spaces in terms of the $$ \mathcal{N}=1 $$ N = 1 superfields, once the Kähler potentials of the base manifolds are obtained. We derive the $$ \mathcal{N}=1 $$ N = 1 supersymmetric nonlinear sigma models on the Kähler manifolds $$ \mathrm{\mathcal{M}} $$ ℳ . Then we extend them into the $$ \mathcal{N}=2 $$ N = 2 supersymmetric models with the use of the result in arXiv:1211.1537 developed in the projective superspace formalism. The resultant models are the $$ \mathcal{N}=2 $$ N = 2 supersymmetric nonlinear sigma models on the cotangent bundles over the Hermitian symmetric spaces $$ \mathrm{\mathcal{M}} $$ ℳ . In this work we complete constructing the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces.